Characterization of the laser induced damage threshold of mirrors in ...

Characterization of the laser induced damage threshold of mirrors in ...

Figure 2.4: Schematic

Figure 2.4: Schematic diagram of avalanche ionization. An initially free electron sequentially absorbs several laser photons through free-carrier absorption, then impact ionizes another electron. From ref. [3] free-carrier absorption. If its energy becomes larger or equal to the conduction band edge energy plus the bandgap energy, it can ionize an atom or ion inthe lattice and thereby generate more conduction band electrons. This is called impact ionization. Both processes are schematically depicted in figure 2.4. Avalanche ionization is a process resulting of an interplay between free-carrier absorption and impact ionization. The more electrons are generated by impact ionization, the more electrons can be heated by free-carrier absorption. Qualitatively is the number of generated new electrons proportional to the number of electrons already inthe CB, leading to an exponential increase ofthe electron density inthe CB. This increase of CB electrons can happen on a much faster scale then the accumulation of CB electrons by multi photon- or tunnel ionization. The relative contributions of multi photon-, tunnel- and avalanche ionization to CB electron generation are still debated [2, 49, 50, 4]. To explainthe dependence ofthe breakdown on pulse duration, photo ionization seeded avalanche was invoked [2, 47, 11, 17]. In contrast, measurements oftheintensity dependent carrier density and the relaxation rates of high-energy CB electrons were interpreted as a result of a small contribution of impact ionization to free-carrier generation.[49] Jupé et al. showed recently [4] that when measuring thedamagethreshold for various wavelengths a clear step inthedamagethreshold can be seen at the transition from two-photon to three-photon absorption. The essential data from that paper are displayed in figure 2.5. They interpret this as clear indicator that for their measurement conditions the breakdown threshold is governed by multi photon absorption. Damage resulting from femtosecond pulses is spatially well confined [2]. This confinement is explained by assuming that the energy inthe CB directly leads to 8

Figure 2.5: Laser induceddamagethresholdof a T iO2 single versus the wavelength. At 680nm, a step ofthe LIDT towards three photon absorption is evident. From ref. [4]. damage 6 without previous coupling to the lattice in form of phonons. Thereby damage is solely caused by the free-carrier density[51, 47], and its spatial extent is given by the free-carrier distribution. Additionally, femtosecond breakdown is very deterministic in that there is only a couple of percent fluence range between damage and no damage. These two aspects make femtosecond damage spatially reproducible and precise to sub micrometers. Femtosecond laser ablation and structuring is used today in a wide field of commercial applications from industry to medicine. Figure 2.6 shows the remarkable difference between fs and ns damage sites. One can see on the fs side a well defined round crater with a sharp transition between crater and surrounding, approximately 40 dielectric layers have been removed in an uniform way. The ns damage on the other hand is quite inhomogeneous. There are regions where the material seems to have melted and re-solidified. In large parts ofthe picture only two or three dielectric layers are removed, giving thedamage site a funnel like topology. 2.2.2 Mathematical modeling ofthe fs damagethreshold Single pulse femtosecond breakdown As previously discussed a critical electron density inthe CB is associated with the breakdown threshold. In order to describe electron densities as a function of time, rate equations have been used. The most general description is given by equation 2.2. Where N(t) denotes the electron density inthe CB and Wi represents an excitation or relaxation rate. 6 the actual mechanism still remains unclear dN(t) dt = Wi (2.2) 9